טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentNir Schreiber
SubjectMonte-Carlo Study of the Baxter-Wu Model
DepartmentDepartment of Physics
Supervisor Dr. Adler Joan


Abstract


We studied the pure and dilute Baxter-Wu models using the Landau-Wang (LW) sampling method to calculate the Density-Of-States. For the pure case, the energy distribution together with its second and fourth moments were calculated to give the specific heat and the reduced energy fourth order cumulant, B, better known as the Binder parameter. The energy distribution displayed a doubly peaked shape. Finite size scaling analysis, however, showed a power low decay of the distance between these peaks to eventually vanish for . It also yielded the expected Baxter-Wu  critical exponent. The Binder parameter minimum appeared to scale with lattice size L , with an exponent  identical with the specific heat exponent and the position (temperature) of the Binder parameter minimum appeared to show a large correction-to-scaling term .  We then introduced impurities to the Baxter-Wu model and  calculated the phase diagram in concentration-temperature plane. Our results, obtained by locating the specific heat maxima, were reliable for low impurities concentrations only, because of small energy fluctuations, characteristic to systems with high amount of disorder, which caused to broader and wider peaks of the specific heat.  For the dilute Baxter-Wu model we found a clear crossover to a single peak in the energy distribution even for small lattice sizes and the expected   was recovered. The Density-Of-States of the two-dimensional Ising model were also calculated and were compared to the exact result. The phase diagram of the dilute two-dimensional Ising model was also calculated and showed good agreement with previous results.